Problem

A bare helium nucleus has two positive charges an…

03:06

Problem 2 Medium Difficulty

An evacuated tube uses an accelerating voltage of 40 kV to accelerate electrons to hit a copper plate and produce x rays. Non-relativistically, what would be the maximum speed of these electrons?

Answer

$v_{e}=1.19 \times 10^{8} \mathrm{m} / \mathrm{s}$

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Physics 102 Electricity and Magnetism

College Physics for AP® Courses

Chapter 19

Electric Potential and Electric Field

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Video Transcript

to solve this question, you must understand what exactly is happening. So we are producing X ray using electrons which are accelerated using the voltage off 40 kilovolt. So it says that what's the maximum speed off electro? So maximum speed of electron, which is accelerated using the so voltage off 40 kilovolt which is 40 times 10 power 10 10 power, three gold. So this is the potential with which we are going to accelerate the charge that is electron so energy produced due to this attention is equal to charge on electron times. The potential difference apply Now this energy will be converted into the kinetic energy. So kinetic energy of electrons is half envy square. So this is K E. So all we have to do is to combine these two that he is equated them too. So half envy square. Now this is a velocity. Let me have some small subscript on it so you don't get confused is equal to any times capital V. So you can see that from this You can simplify this equation as two times Elektronik charge times the voltage applied or the potential different supply divided by mass. So let's calculate this because we know some values from this. We know that Electron has a charge off one points. Extremes. Jen Power Negative 19. Walter Supplied is 40. Killer would that is for a few times 10. Power three Divided by massive Philip Tron is 9.11 times 10 Power Negative. 31. So let me calculate this on the calculator. Two times, 1.6 times 40 divided by 9.11 Excuse me is square root 14 point all five times. Now let's calculate, Let's count how many What's the power of 10? So from negative 31 negative 19 you get positive well and from positive three. You get 15 so you can simplify this on DDE. If you take the square root off this answer, you will get 1.18 times 10 power, eight meters per second. So, as in question, it says that did not take relativistic effects into account that is non relativistic, even if if it was considered relativistic. This velocity is possible for electron because this is less 10 speed off light. As you know, speed off light see is given by three times 10 power eight me trespass seconds so called into relativistic principle. The speed is possible

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